1. Field of the Invention
The present invention refers to a filter and a method for filtering communication signals, and more particularly to an ideal-like band-pass filter and single-frequency filter which is characterized in Frequency Response Formula and Phase-Shift Response Formula.
2. Description of the Prior Art
For those conventional filters, no matter analog (not periodical) or digital (periodical), their frequency response formulae and phase-shift response formulae always generate different amplitudes of vibrations and different phase-shifts according to different frequencies of sine signals.
Conventional methods for designing filters mostly are related to the application of differential or difference equations. Firstly, a linear system representing the relationship between input and output signals is established, and then the output signal of this system can be calculated. This system can be established by electric circuitries, but also can be simulated by mathematics. Because the operations of circuitries (or operations of mathematical simulations) in the system always involve in actions of delayed signals (or advanced signals), which are actually resulted from the operations of capacitors (or inductors). That's why conventional filters always generate different amplitudes of vibrations and different phase-shifts according to different frequencies of sine signals.
Until now, the ways to avoid the phenomenon of aforementioned variations of amplitudes and phase-shifts are still focal points in designing the filters.
In addition, for conventional band-pass filters, the leading and rear edges of each curve of responsive frequency formulae are still not steep enough, which result in unclear borderlines between the responsive frequencies and the unresponsive frequencies, and thus require further improvements.